RE: completeness

Hi Peter!

>> >Nor does
>> >
>> >p r q .
>> >
>> >pD* entail
>> >
>> >p rdf:type _:e .
>> >_:e owl:hasValue q .
>> >_:e owl:onProperty r .
>> 
>> This entailment is actually explicitly supported by pD*. In 
>this case even
>> the converse entailment exists (a rare case of 
>"iff"-semantics in pD*). The
>> respective semantic condition is given by Definition 5.1 in [10]:
>> 
>>   If 
>>     (a, b) in E_I(I(hasValue)) 
>>     and (a, p) in E_I(I(onProperty)), 
>>   then 
>>       x in CE_I(a) 
>>     if and only if 
>>       (x, b) in E_I(p),
>> 
>> where "E_I(.)" denotes a property extention, and "CE_I(.)" 
>denotes a class
>> extention.
>
>No.
>
>The entailment does not go through because there need not be a,b,p such
>that 
>	(a, b) in E_I(I(hasValue)) 
>	(a, p) in E_I(I(onProperty))
>in models of
>	p r q .

("x p b" for some given x).

Yes, you are right! The existence of the class a, which is defined by the HasValue restriction, doesn't result alone from the stated triple. I must have confused the situation here with OWL-Full, where there is a comprehension principle, which gives me this class alone from having the property p and the value b.

After reading your answer, I first thought that this semantic condition of pD* must thus be pretty useless, since the need for explicitly stating HasValue restrictions looked cumbersome to me. However, I found that it has its benefits, anyway. For example, I can state TBox axioms such as

  _:x rdf:type owl:Restriction .
  _:x owl:onProperty zoo:hasBodyPart .
  _:x owl:hasValue zoo:fur .
  _:x rdfs:subClassOf zoo:Mammal .

Now, if the RDF graph contains the triple

  :chita zoo:hasBodyPart zoo:fur .

then pD* allows me to entail

  :chita rdf:type zoo:Mammal .

IMHO not bad for a language with such weakly defined semantics. :)

Cheers,
Michael

--
Dipl.-Inform. Michael Schneider
FZI Forschungszentrum Informatik Karlsruhe
Abtl. Information Process Engineering (IPE)
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